Which of the following comes closest to the value at the end of year 6 of investing $600 today (year 0) and then investing anoth
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Answer:
Ans. c) Discounted period is 1.01 years longer than payback period.
Explanation:
Hi, the payback period is the time that takes for the initial invesment to return to the investor (regardless of the time value of money), so we add the cash flow for every period until the result is zero.
The discounted payback period is almost the same, here we do take into account the time value of money. let´s check out the math to this.
Payback period
Period Cash Flow Adding cash flows Coefficient Payback
0 -$50,000.00 -$50,000.00 3
1 $15,000.00 -$35,000.00 1
2 $15,000.00 -$20,000.00 1
3 $20,000.00 $- 1
4 $10,000.00
5 $5,000.00
Payback period = 3
Discount rate 8%
Period Cash Flow Present Value Adding Cash Coefficient
0 -$50,000.00 -$50,000.00 -$50,000.00
1 $15,000.00 $13,888.88 -$36,111.11 1
2 $15,000.00 $12,860.08 -$23,251.03 1
3 $20,000.00 $15,876.64 -$7,374.38 1
4 $10,000.00 $7,350.29 -$24.09 1
5 $5,000.00 $3,402.91 0.01
Discounted payback period = 4.01
The only thing here that needs some further explanation is the 0.01, this is by doing the following calculation.
This is the fraction of the year that will turn those $24.09 in zero (taking into account the cash flow of period 5 which is 3402.91)
So, discounted payback period - Payback period= 4.01 - 3 = 1.01
Best of luck.